IN April, Gov. Jerry Brown made headlines by signing into law an ambitious mandate that requires California to obtain one-third of its electricity from renewable energy sources like sunlight and wind by 2020. Twenty-nine states and the District of Columbia now have renewable electricity mandates. President Obama and several members of Congress have supported one at the federal level. Polls routinely show strong support among voters for renewable energy projects — as long as they don’t cost too much.

But there’s the rub: while energy sources like sunlight and wind are free and naturally replenished, converting them into large quantities of electricity requires vast amounts of natural resources — most notably, land. Even a cursory look at these costs exposes the deep contradictions in the renewable energy movement.

Consider California’s new mandate. The state’s peak electricity demand is about 52,000 megawatts. Meeting the one-third target will require (if you oversimplify a bit) about 17,000 megawatts of renewable energy capacity. Let’s assume that California will get half of that capacity from solar and half from wind. Most of its large-scale solar electricity production will presumably come from projects like the $2 billion Ivanpah solar plant, which is now under construction in the Mojave Desert in southern California. When completed, Ivanpah, which aims to provide 370 megawatts of solar generation capacity, will cover 3,600 acres — about five and a half square miles.

The math is simple: to have 8,500 megawatts of solar capacity, California would need at least 23 projects the size of Ivanpah, covering about 129 square miles, an area more than five times as large as Manhattan. While there’s plenty of land in the Mojave, projects as big as Ivanpah raise environmental concerns. In April, the federal Bureau of Land Management ordered a halt to construction on part of the facility out of concern for the desert tortoise, which is protected under the Endangered Species Act.

Wind energy projects require even more land. The Roscoe wind farm in Texas, which has a capacity of 781.5 megawatts, covers about 154 square miles. Again, the math is straightforward: to have 8,500 megawatts of wind generation capacity, California would likely need to set aside an area equivalent to more than 70 Manhattans. Apart from the impact on the environment itself, few if any people could live on the land because of the noise (and the infrasound, which is inaudible to most humans but potentially harmful) produced by the turbines.